Abstract
This study presents the double Fourier cosine series method for
solving the flexural problem of Kirchhoff plates resting on an
elastic foundation of the Winkler type. The problem is a boundary
value problem represented by a fourth order partial differential
quantum. For the case of simply supported edges, the Dirichlet
boundary conditions are identically satisfied by double Fourier
cosine series if the plate centre becomes the origin of the
Cartesian coordinates. A Fourier cosine series assumption for the
unknown deflection function and the known load distribution
results in an algebraic problem for the unknown Fourier
parameters of the series; which is solved to obtain the deflection
function. The paper presents general solutions for deflection and
bending moments for arbitrary transverse load distribution and
specific solutions for the deflections and bending moments for the
specific cases of point load at arbitrary point, and at the centre,
uniformly distributed load over the entire plate and sinusoidal
load. It was found that the solutions obtained in this study were
exact solutions and this was because the double Fourier cosine
series used for the deflection shape functions were exact shape
functions that satisfies all the Dirichlet boundary conditions.
Furthermore, the trial solution was made to satisfy the boundary
value problem at all points in the solution domain.
Keywords:
Double Fourier cosine series, Kirchhoff plate, Winkler
foundation, Boundary value problem
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Abstract
For most of the tunnels, the rock-support interface can vary
between some full-slip to a non-slip condition, so both types should
be investigated for static lining forces and deformations. In
dynamic analysis, these conditions have a deterministic role on the
interaction between the tunnel periphery rock mass and tunnel
lining and evidently, on the load transfer intensity between them.
In this paper, a dynamic analysis of tunnels under different
conditions of the rock mass and lining interface has been carried
out by analytical and FEM numerical methods. Also, the effect of
the interface between tunnel lining and surrounding medium on
earthquake intensity studied. In the following, the numerical results
are verified based on an analytical method. The numerical and
analytical results have a meaningful agreement with themselves.
Results also showed that tunnel lining is more confronted with the
induced stress due to the earthquake shake forces in non-slip
condition, while in medium it is the other way around.
Keywords:
Interface, Full-Slip, Non-Slip, Earthquake Loading,
Tunnel Lining
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response of tunnel with different lining rigidity based on Finite
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conditions", European Journal of Environmental and Civil
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Abstract
Presented in this paper is an implicit finite difference solution for
radial flow consolidation to prefabricated vertical drains (PVDs)
under haversine cyclic loading with rest period assuming no smear
and a constant coefficient of consolidation. Such long-term cyclic
loads are induced by traffic on highways, airports and railway
tracks. The effect of duration ratio of rest period to that of
loading-unloading phase within a cycle, of 0 ,1 and 2, on the time
variation of excess pore water pressure and effective stress was
studied thoroughly. The effect of PVD spacing expressed by the
ratio of radius of influence zone of drain well to that of PVD was
studied for three different values of 5, 10 and 40. The findings
revealed that for any rest period, the excess pore water pressure
oscillates changing sign with time although the imposed loading is
always positive. The oscillation comes to almost steady state at a
time factor of unity. The effective stress increases with time but
with some fluctuation without changing sign. The average curve
for the region between the upper bound and lower bound of
effective stress curve with time converges to the average of
haversine cyclic loading with rest period (having amplitude q0),
namely q0/2 ,q0/4 and q0/6 for the ratio of rest period to that of
loading-unloading phase of 0, 1 and 2 respectively. This is
independent of the time factor value at the end of first
loading/unloading phase. This indicates that longer rest periods
decrease the total primary consolidation settlement due to cyclic
loading.
Keywords:
Cyclic loading, Prefabricated vertical drains, Radial
flow consolidation, Rest period, Wick drains
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Abstract
The road construction industry is concerned with utilizing
alternative and sustainable binder materials to aid in the production,
placement and increase in the performance of flexible pavements.
This research is aimed at evaluating the physical properties of
bituminous mixtures modified with PET (Polyethylene
Terephthalate), SBS (Styrene-Butadiene-Styrene) and EVA
(Ethylene-vinyl Acetate) used as bitumen modifiers. The samples
were prepared by heating the base bitumen and each polymers to
their respective melting points to facilitate the miscibility of the
materials; the base bitumen and each polymers were mechanically
mixed together with a blending speed of 2000 ± 10 rpm for an hour.
Penetration, ductility, softening point, flash and fire point and water
in bitumen tests were performed to relevant standard specifications
on bitumen and PMB (Polymer Modified Bitumen) with polymer
composition varied from 10% to 50%. The penetration test result
showed that polymers have hardening effect on bitumen; this was
evidenced by the reduction in the penetration values of PET
modified bitumen from 51 to 57 decimillimetre (dmm), 59 to 55
dmm for SBS modified bitumen and 68 to 59 dmm for EVA
modified bitumen for all the percentage compositions. The PMB
showed improved stiffening which was demonstrated by increase
in the softening point of the PMB; the softening point of PET
modified bitumen increased from 540C to 670C. Likewise, the
softening point of SBS modified bitumen increased from 560C to
700C and the softening point of EVA modified bitumen also
increased from 550C to 600C for all the percentage polymer
compositions. The improvement in the water resistant capability of
the PMB was confirmed by the reduction of moisture content of
bitumen on addition of polymers from 3% for bitumen to 1.1%
which is the least moisture content recorded at 50% composition of
SBS modified bitumen.
Keywords:
Physical properties, polymer additives, bitumen, bituminous mixture
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Abstract
Monitoring and controlling soil behavior during the excavation of
new tunnel nearby the existent tunnel is so crucial in providing
safety for adjacent structures. The interaction between excavating
tunnel (line 2) underneath the present metro station (Line 1) in
their intersection was examined in this study. To simulate the
conditions of stress and displacement caused by excavating over
the current station, the process of tunnel excavation is modeled by
Cut & Cover method. For the station's foundation, the pile-raft
system is used to reduce settlement and the effects of interaction
between the station and the new tunnel. The new tunnel under the
station has been surrounded by soldier beams (soldier piles) in a
distance of 20 cm from the tunnel wall. In the design phase for the
tunnel Line 2 which will be excavated using a TBM-EPB (Tunnel
Boring Machine-Earth Pressure Balance), the control of station’s
safety near this line is a principle. Therefore, exploring the
interaction between the excavating tunnel and the present station
and also assessing the surface settlement in this area are of great
importance. To investigate this mechanism, the limited threedimensional
components analysis is applied by employing Abaqus
6-10.1 software. The Mohr-Coulomb Behavioral model is used
for the soil. Results show that by the usage of pile-raft system, the
surface settlement resulting from the excavation of new tunnel is
reduced. Also, the results demonstrate a decline in the relative
difference in terms of settlement over the raft.
Keywords:
metro station, tunneling by TBM-EPB, settlement, Finite element, three-dimensional modeling
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